Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
338 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21462176 | C2 | semidirect |
| 2. C4×#14519851 | C2 | semidirect |
| 3. #21460787 | C2 | semidirect |
| 4. #21460771 | C2 | semidirect |
| 164. C61 | #11617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462176 | 2 |
| C4×#14519851 | 2 |
| #21460787 | 2 |
| #21460771 | 2 |
| #21454786 | 2 |
| #11617 | 61 |